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[Membership] Voting systems: Approval voting


I looked at your report.htm  
I think there are better options than the voting systems proposed so far.

May I contribute this as an alternative and possibly superior voting system?
(Mike Saari's paper)
Discussion invited.


Suppose a group of rational, intelligent people is trying to make a choice
amongst several alternatives.  Will their voting system give them a
consistent (and good) outcome?  For virtually every voting system in use
today, the answer is, sadly, NO.  This paper demonstrates this simple but
startling conclusion. 

Fortunately there is a solution (which I will also describe). 

Let's construct a simple voting scenario.  Suppose the choice is between
two viable candidates/propositions/flavors "A" and "B". Using a particular
voting system and assuming only A and B are on the ballot, suppose that A
consistently wins each election.  Now let's repeat the very same vote, but
with additional alternatives "X, Y, Z, etc." on the ballot as well. 

If a case can be demonstrated where B wins over A, then I assert that that
voting system is fatally flawed, because it is not accurately recording
the preferences of the voters. 

[Two classes of additional candidates that easily stress any voting system
are any numbers of "Bozos" and/or "Twins".  A "Bozo" is any mediocre
candidate.  A "Twin" is a candidate which is identical and
indistinguishable from another particular candidate.  Given a choice
between two Twins, assume that voters will choose randomly, since either
"Twin" outcome is equally good.]

To demonstrate a typical flawed voting system, take the common "simple
plurality" method (vote for one candidate, and the highest total wins). 
For the simple A vs. B case, assume that A consistently wins (A=60%,
B=40%).  Now we add an indistinguishable, identical twin (A') to the
ballot and re-vote.  The likely outcome is that B wins (A=30%, A'=30%,
B=40%).  Thus, this system is flawed. 

Adding a "runoff" stage to the previous "vote for one candidate" system
(the other common "solution") doesn't work either!  The proof, you say? 
For the same scenario as before (A wins 60%- 40%), let's add nine "A"
Twins and one "B" Twin.  Each version of A will get 6% of the vote, and
each B twin will get 20%.  The runoff will be between B and B', and the
result is again flawed. 

Various more complex schemes are often proposed, and most have been tried. 
But the same flaw can be demonstrated with every other "ranked"-type
voting system. 

I invite the reader to try out the "Twin/Bozo" stress test against their
favorite "other voting system".  Here is an excellent "Litmus test"
example to work with: 

Suppose that all voters in the group rate (subjectively, but honestly)
candidate B as "Very, Very Good".  60% of the group rate candidate A as
"Excellent", but a large 40% minority rate candidate A as "Awful".  (Which
candidate is really "best" is ambiguous but that's not the issue here;
only whether adding choices could alter the outcome under a given voting

For the simple one-vote system (with or without runoff), the flaw is
demonstrated as described above. 

Take ranked "Borda Voting" as another popular suggestion.  (Borda Voting
means that, with 5 candidates, everybody ranks their choices first,
second, third, fourth, fifth.  Each "first" vote earns 5 points for that
candidate; each "second" vote earns 4 points, etc.) A wins in the simple
case, but adding several Bozos to the ballot will shift the result to B. 
Borda is therefore flawed. 

Every other proposed system of ranked voting (such as successive-
elimination and other even-more-hopelessly-complex schemes) can also be
shown to be flawed in a similar manner. 

"ranked") systems. 

"Approval Voting" (vote yes or no for each candidate, then a simple tally)
is the simplest voting system which is not fundamentally flawed.  My
personal favorites are "Offset Approval (vote each candidate with a number
between +10 and -50)" and "Rational Approval (vote yes or no for each
candidate, and divide the yes count by the no count)". 

Let's see how basic "Approval Voting" holds up against the "Litmus Test". 
Clearly, the 40% minority that hates A will probably vote A=NO/B=YES for
the simple A-B case. 

The other 60% will vote either A=YES/B=YES ("They're both quite
qualified.") or A=YES/B=NO ("B isn't good enough for me.") Depending on
the overall distribution of these votes (which depends on the sense of the
group as to whether or not "Very Good" is good enough for the task at
hand), either A or B could win this contest. 

However, seeing lots of Bozos is unlikely to change any particular voter's
vote, whatever it was!  And if the voter used to vote yes for A and now
there are five indistinguishable "A" Twins on the ballot, they will simply
vote yes for all of them.  Result: NO FLAW. 

CONCLUSION: "Approval Voting" (or its variations) will produce consistent,
rational results for any situation of group decision- making.  ANY OTHER
committee") AND/OR IS SUBJECT TO RANDOM DISTORTIONS (depending on the
chance distributions of candidates).